A frequency-time domain stability criterion for sampled-data systems

An improved sufficient condition developed for the asymptotic stability of a sampled-data system having a single monotonic nonlinearity, with a slope in the sector<tex>(0, k_{2})</tex>and a pulse transfer function<tex>G^{\ast}(z)</tex>, is<tex>Re [(1+X^{\ast}(z)+Y^{\ast}(z))(G^{\ast}(z)+I/k_{2})]\geq0</tex>for<tex>z</tex>on the unit circle, where<tex>x(i) \leq 0</tex>for<tex>i<0</tex>and<tex>x(i)=0</tex>for<tex>i>0, y(i) \leq 0</tex>for<tex>i\geq0</tex>and<tex>y(i)=0</tex>for<tex>i<0</tex>, and<tex>\Sigma\min{i=-\infty}\max{+\infty} \|x(i) + y(i)\| < 1</tex>. An improved frequency domain condition is also presented for the case of the nonlinearity being odd as well as monotonic.